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أوجد المشتق العكسي لـ
∫2xx2+2dx\int_{ }^{ }\frac{2x}{x^2+2}dx∫x2+22xdx
ln∣x2+2∣+1x+c\ln\left|x^2+2\right|+\frac{1}{x}+cln∣∣x2+2∣∣+x1+c
ln∣x2+2∣+c\ln\left|x^2+2\right|+cln∣∣x2+2∣∣+c
ln∣x+1x∣+c\ln\left|\frac{x^{ }+1}{x}\right|+cln∣∣xx+1∣∣+c
قيّم التكامل
∫2x2x+1dx\int_{ }^{ }\frac{2x^2}{x+1}dx∫x+12x2dx
x2−2xln∣4x∣+cx^2-2x\ln\left|4x\right|+cx2−2xln∣4x∣+c
4ln∣x∣+c4\ln\left|x\right|+c4ln∣x∣+c
x2−2x+2ln∣x+1∣+cx^2-2x+2\ln\left|x+1\right|+cx2−2x+2ln∣x+1∣+c
أكمل هذا البيان
إذا كان f (x)=Cos x و g(x)=loglogx
إذن
∫[f(x) -g(x)] dx = ___________.
2x2cosx−xloglogx+c2x^2\cos x-x\log\log x+c2x2cosx−xloglogx+c
sinx+xloglogx−x+c\sin x+x\log\log x-x+csinx+xloglogx−x+c
cosx−xloglogx+x+c\cos x-x\log\log x+x+ccosx−xloglogx+x+c
∫x+1x−2dx\int_{ }^{ }\frac{x+1}{x-2}dx∫x−2x+1dx
(x+3)ln∣x+1∣+c\left(x+3\right)\ln\left|x+1\right|+c(x+3)ln∣x+1∣+c
(x−3)ln∣x+1∣+c\left(x-3\right)\ln\left|x+1\right|+c(x−3)ln∣x+1∣+c
x+ln∣x−2∣+cx+\ln\left|x-2\right|+cx+ln∣x−2∣+c
∫xx2+2x+1dx\int_{ }^{ }\frac{x}{x^2+2x+1}dx∫x2+2x+1xdx
ln∣x+1∣+c\ln\left|x+1\right|+cln∣x+1∣+c
ln∣x+1∣+1x+1+c\ln\left|x+1\right|+\frac{1}{x+1}+cln∣x+1∣+x+11+c
−19x9+c-\frac{1}{9x^9}+c−9x91+c
∫(1−2x)x2(x+1)dx\int_{ }^{ }\frac{\left(1-2x\right)}{x^2\left(x+1\right)}dx∫x2(x+1)(1−2x)dx
ln∣x+1x∣+1x+c\ln\left|\frac{x+1}{x}\right|+\frac{1}{x}+cln∣∣xx+1∣∣+x1+c
(1−2x)2(x−2)2+c\frac{\left(1-2x\right)}{2\left(x-2\right)^2}+c2(x−2)2(1−2x)+c
ln∣x+1x∣−1x+c\ln\left|\frac{x+1}{x}\right|-\frac{1}{x}+cln∣∣xx+1∣∣−x1+c
إذا كان
f (x)=Cos x و g(x)=x3
فإن
∫[f(x) - g(x)] dx = ___________.
x22+sinx+c\frac{x^2}{2}+\sin x+c2x2+sinx+c
sinx+14x4+c\sin x+\frac{1}{4}x^4+csinx+41x4+c
sinx−14x4+c\sin x-\frac{1}{4}x^4+csinx−41x4+c
∫2x+3x2−9dx\int_{ }^{ }\frac{2x+3}{x^2-9}dx∫x2−92x+3dx
ln∣x2∣−2x+2ln∣x+1∣+c\ln\left|x^2\right|-2x+2\ln\left|x+1\right|+cln∣∣x2∣∣−2x+2ln∣x+1∣+c
12ln∣(x−3)2(x+3)∣+c\frac{1}{2}\ln\left|\left(x-3\right)^2\left(x+3\right)\right|+c21ln∣∣(x−3)2(x+3)∣∣+c
إذا كانت
f (x)=5x3 و g(x)=2x2
54x4+ex+c\frac{5}{4}x^4+e^x+c45x4+ex+c
54x4−23x3+c\frac{5}{4}x^4-\frac{2}{3}x^3+c45x4−32x3+c
54x4+73x3+x+c\frac{5}{4}x^4+\frac{7}{3}x^3+x+c45x4+37x3+x+c
f (x)=Sinx و g(x)=loglogx
−cosx+xloglogx−x+c-\cos x+x\log\log x-x+c−cosx+xloglogx−x+c
−cosx−xloglogx+x+c-\cos x-x\log\log x+x+c−cosx−xloglogx+x+c
إنتهى الإختبار.